Depends on your stats and proficiency, but best case is about 10-25%
For the most part, the difficulty is based on the level of the monster using this chart. As you can see, it is anywhere from level + 14 to level +25. This can be further modified by creature rarity, with uncommon creatures adding +2, and rare adding +4 or 5, and so on.
So, in order to crit, you will need to keep your proficiency level maxed and your Wis high. At level 1 (+1), with a trained skill (+2), a 14 Wis (+2) (using your +5 Nature skill comment), reaching the DC 15 check for a common creature would require a D20 roll of 10, and critting it would thus require a roll of 20, for a 5% chance of critting. If you get expert at level 3, you can crit on a 19 until level 6, and this fluctuation continues (master at 7 allows you to crit on a 18, etc). If you invest more into your starting Wis, then you can bump your odds by 5% (16 is the max Wis you can start with as a Ranger). If you have the Outwit Hunter's Edge (thanks Ifusaso), you can up your odds by an additional 10% due to the +2 to Recall Knowledge checks it grants against your prey (and since Monster Hunter is triggered when using Hunt Prey, that's always going to be the case).
This assumes that the GM uses the DC by level chart referenced or the DCs suggested in the Monstrous Manual. Also, this assumes equal leveled monsters. Your odds go up with lower level monsters (which you may encounter often, but might be easy enough to defeat that using an action in this way might not be worthwhile in most cases) and down with higher level monsters.
To summarize, for equal level creatures, if you start with a 14 Wis and always up your Nature proficiency at the earliest opportunity, you need to roll between a 17 and a 20 to crit (5-20% chance), depending on the level you and the monster are at. If you start with a 16 Wis, you can up that by 5% (10-25% chance). If you are an Outwit Hunter, you can crit 20-35% of the time. This is of course worse for any skill (Occult, Arcane, Religion) that you are not keeping up on as diligently. And, since it is only a single action to Hunt Prey, you can do this every turn with your third action if you like (usually in lieu of a third attack that has little chance of hitting).